Question
If
be any point on a line then the range of for which the point ' P ' lies between the parallel lines x+2y=1 and 2x+4y=15 is
![fraction numerator negative 4 square root of 2 over denominator 3 end fraction less than alpha less than fraction numerator 5 square root of 2 over denominator 6 end fraction](data:image/png;base64,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)
![0 less than alpha less than fraction numerator 5 divided by square root of 2 over denominator 6 end fraction](data:image/png;base64,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)
![fraction numerator negative 4 square root of 2 over denominator 3 end fraction less than alpha less than 0](data:image/png;base64,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)
- None of these
Hint:
When a point is existing in between two lines the product of it's values with respect to the point will always gives negative. Because, the the property of a line with respect to point changes for two lines.
The correct answer is: ![fraction numerator negative 4 square root of 2 over denominator 3 end fraction less than alpha less than fraction numerator 5 square root of 2 over denominator 6 end fraction](data:image/png;base64,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)
Given That:
If
be any point on a line then the range of for which the point ' P ' lies between the parallel lines x+2y=1 and 2x+4y=15 is
>>> When a point lies in between the lines. Then:
L11.L22 <0
>>> L11 becomes: (1+
)+2(
) -1
>>> L22 becomes : ![2 left parenthesis 1 plus fraction numerator alpha over denominator square root of 2 end fraction right parenthesis plus 4 left parenthesis 2 plus fraction numerator alpha over denominator square root of 2 end fraction right parenthesis minus 15](data:image/png;base64,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)
>>> Therefore:
L11.L22 < 0
((1+
)+2(
) -1).(
) < 0
>>> This gives range as
.
((1+)+2(
) -1).(
) < 0
Related Questions to study
is any point in the interior of the quadrilateral formed by the pair of lines and the two lines 2x+y-2=0 and 4x+5y=20 then the possible number of positions of the points ' P ' is
is any point in the interior of the quadrilateral formed by the pair of lines and the two lines 2x+y-2=0 and 4x+5y=20 then the possible number of positions of the points ' P ' is
If the point
,lies in the region corresponding to the acute angle between the lines 2y=x and 4y=x then - .....
u ≡ x - 2y = 0 and v ≡ x - 4y = 0
>>> S(x, y) ≡ x² - 6xy + 8y² = 0
>>> ( a - 2 )( a - 4 ) < 0
If the point
,lies in the region corresponding to the acute angle between the lines 2y=x and 4y=x then - .....
u ≡ x - 2y = 0 and v ≡ x - 4y = 0
>>> S(x, y) ≡ x² - 6xy + 8y² = 0
>>> ( a - 2 )( a - 4 ) < 0
Consider A(0,1) and B(2,0) and P be a point on the line 4x+3y+9=0, co-ordinates of P such
is maximum is
Hence the point is (,
).
Consider A(0,1) and B(2,0) and P be a point on the line 4x+3y+9=0, co-ordinates of P such
is maximum is
Hence the point is (,
).
Assertion (A): The lines represented by
and x+ y=2 do not form a triangle
Reason (R): The above three lines concur at (1,1)
Both Assertion and Reason are correct and the Reason is the correct explanation of Assertion.
Assertion (A): The lines represented by
and x+ y=2 do not form a triangle
Reason (R): The above three lines concur at (1,1)
Both Assertion and Reason are correct and the Reason is the correct explanation of Assertion.
In Bohr’s hydrogen atom, the electronic transition emitting light of longest wavelength is:
In Bohr’s hydrogen atom, the electronic transition emitting light of longest wavelength is:
P1,P2,P3, be the product of perpendiculars from (0,0) to
respectively then:
P1 = 1;
P2 = ;
P3 = ;
>>> Therefore, we can say that P1>P2>P3.
P1,P2,P3, be the product of perpendiculars from (0,0) to
respectively then:
P1 = 1;
P2 = ;
P3 = ;
>>> Therefore, we can say that P1>P2>P3.
If θ is angle between pair of lines
, then ![cosec squared invisible function application theta equals](data:image/png;base64,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)
>>> = 2.
>>> tan =
>>> = 10.
If θ is angle between pair of lines
, then ![cosec squared invisible function application theta equals](data:image/png;base64,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)
>>> = 2.
>>> tan =
>>> = 10.
If the pair of lines
intersect on the x-axis, then 2fgh=
If the pair of lines
intersect on the x-axis, then 2fgh=
If the pair of lines
intersect on the x-axis, then ac=
If the pair of lines
intersect on the x-axis, then ac=
If the equation
represents a pair of perpendicular lines then its point of intersection is
If the equation
represents a pair of perpendicular lines then its point of intersection is
If the lines
and
are concurrent then λ
>>> The value of is 2.
If the lines
and
are concurrent then λ
>>> The value of is 2.
The equation of the line concurrent with the pair of lines
is
Hence, x=y is the the line that is concurrent with the pair of straight lines.
The equation of the line concurrent with the pair of lines
is
Hence, x=y is the the line that is concurrent with the pair of straight lines.
If the equation
represents a pair of straight lines then their point of intersection is
>>>The point of intersection of the pair of straight lines x2 – 5xy + 6y2 + x – 3y = 0 is (-3, -1)
If the equation
represents a pair of straight lines then their point of intersection is
>>>The point of intersection of the pair of straight lines x2 – 5xy + 6y2 + x – 3y = 0 is (-3, -1)